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The given problem provides a function \( f(x) = \frac{150 - 20x}{x} \) and asks to find \( f\left(\frac{2}{3}\right) \) and \( f(-3) \).

Let's calculate these values step-by-step.

### 1. Calculate \( f\left(\frac{2}{3}\right) \):
\[ f\left(\frac{2}{3}\right) = \frac{150 - 20\left(\frac{2}{3}\right)}{\frac{2}{3}} \]
Simplify the numerator:
\[ 150 - 20\left(\frac{2}{3}\right) = 150 - \frac{40}{3} = \frac{450}{3} - \frac{40}{3} = \frac{410}{3} \]

Now divide by \( \frac{2}{3} \):
\[ f\left(\frac{2}{3}\right) = \frac{\frac{410}{3}}{\frac{2}{3}} = \frac{410}{3} \times \frac{3}{2} = \frac{410}{2} = 205 \]

So, \( f\left(\frac{2}{3}\right) = 205 \).

### 2. Calculate \( f(-3) \):
\[ f(-3) = \frac{150 - 20(-3)}{-3} \]
Simplify the numerator:
\[ 150 - 20(-3) = 150 + 60 = 210 \]

Now divide by \(-3\):
\[ f(-3) = \frac{210}{-3} = -70 \]

So, \( f(-3) = -70 \).

### Final Answers:
1. \( f\left(\frac{2}{3}\right) = 205 \)
2. \( f(-3) = -70 \)

Would you like more details on any of the steps or have additional questions?

### Related Questions:
1. How do you simplify complex fractions step-by-step?
2. What are the properties of rational functions?
3. How do you find vertical and horizontal asymptotes of a function like \( f(x) \)?
4. What is the domain and range of the function \( f(x) = \frac{150 - 20x}{x} \)?
5. How do you determine critical points for \( f(x) \)?

**Tip:** Always check the domain of a function before calculating specific values, especially for rational functions where the denominator can be zero.

Find f(2/3) and f(-3) for the function f(x) = (150 - 20x) / x.

Learn how to evaluate the rational function f(x) = (150 - 20x) / x for specific values of x. This step-by-step solution walks through finding f(2/3) and f(-3), highlighting key algebraic concepts like substitution and rational expressions.

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